Fractionally Spaced Equalization of Nonlinear Channels

分数间隔均衡(FSE)是指在一般满足的条件下，对信道输出进行分数采样可以从信道输出的二阶统计量中进行识别，因此分数间隔均衡(FSE)已经成为人们关注的焦点。在衰落的多径环境中，盲方案又是可取的，其中信道动态的频繁变化使得训练信号非常浪费。大多数分数间隔盲均衡文献都是关于线性信道的。然而，许多频道，如带有非线性放大器的卫星和微波频道，水下和磁记录频道，本质上是非线性的。如果功放工作在最省电的状态下，情况尤其如此。此外，在光纤通信中，具有充足的带宽的最大挑战是信道中的色散非线性。在许多这样的情况下，盲均衡是自然的，考虑非线性信道的盲FSE是很重要的。本研究涉及FIR信道的盲分数间隔均衡，其特征是基带信道输出是当前和过去输入值的多项式函数。所寻求的均衡器也属于这一类。利用非线性系统互素性的概念，利用差分代数技术，对这类信道的均衡进行了基础性的研究。正在探索这些信道是可均衡的并且可以由输出的二阶统计量识别的条件。研究采用了统计方法和确定性方法。提出了直接均衡器和间接均衡器的设计方法。设计了迫零均衡器和最小均方误差均衡器。使用了子空间方法。适应性方案是假定的。考虑了基本的存在问题以及实际的设计问题。

Fractionally Spaced Equalization (FSE) has become the focus of much research attention since the discovery that fractionally sampling the output of a channel permits its identification from the second-order statistics of the channel output under generically satisfied conditions. Blind schemes in turn are desirable in fading multipath environments where frequent changes in the channel dynamics, makes training signals very wasteful. Most of the blind Fractionally Spaced Equalization literature has been devoted to linear channels. Yet many channels such as satellite and microwave channels with nonlinear amplifiers, underwater and magnetic recording channels are inherently nonlinear. This is particularly so if the amplifiers operate in their most power efficient regimes. Further, in fiber optical communications, having an abundant bandwidth, the greatest challenge, is posed by dispersive nonlinearities in the channel. In many such instances blind equalization is natural and it is important to consider blind FSE of nonlinear channels.This study concerns the blind Fractionally Spaced Equalization of FIR channels characterized by a baseband channel output that is a polynomial function of the current and past values of the input. The equalizers sought also belong to this class. Using the concept of coprimeness of nonlinear systems, and employing difference algebraic techniques, a fundamental investigation into the equalization of this class of channels is being conducted. Conditions under which these channels are equalizable, and can be identified by the second order statistics of the output are being explored. Statistical and deterministic methods are employed. Direct and indirect equalizer design methodologies are formulated. Zero Forcing and Minimum Mean Squared Error equalizers are designed. Subspace methods are used. Adaptive schemes are postulated. Fundamental existence issues as well practical design issues are considered.